SOLUTION: Age of 2 friends Ram and Karan differ by 3 years. Ram's father Dharam is twice as old as Ram and Karan is twice as old as his sister Gita. The ages of Gita and Dharan differ by 30

Algebra ->  Linear-equations -> SOLUTION: Age of 2 friends Ram and Karan differ by 3 years. Ram's father Dharam is twice as old as Ram and Karan is twice as old as his sister Gita. The ages of Gita and Dharan differ by 30       Log On


   

Question 924764: Age of 2 friends Ram and Karan differ by 3 years. Ram's father Dharam is twice as old as Ram and Karan is twice as old as his sister Gita. The ages of Gita and Dharan differ by 30 years. Find the age of Ram.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Age of 2 friends Ram and Karan differ by 3 years.
Ram's father Dharam is twice as old as Ram and Karan is twice as old as his sister Gita.
The ages of Gita and Dharan differ by 30 years.
Find the age of Ram.
:
let r = R's present age
let k = K's present age
let d = father's age
let g = G's age
:
Write an equation for each statement
:
"Age of 2 friends Ram and Karan differ by 3 years."
r - k = 3
r = k + 3
:
" Ram's father Dharam is twice as old as Ram"
d = 2r
:
" and Karan is twice as old as his sister Gita."
k = 2g
:
" The ages of Gita and Dharan differ by 30 years."
d - g = 30
d = g + 30
:
In the equation d = 2r, replace r with (k+3
d = 2(k+3)
in d = g + 30, replace d with 2(k+3)
2(k+3) = g + 30
replace k with 2g
2(2g+3) = g + 30
4g + 6 = g + 30
4g - g = 30 - 6
3g = 24
g = 8
then
k = 2(8) = 16
and
r = 16 + 3
r = 19 yrs is Ram's age